REG2006 méthode réglementaire de calcul thermique des bâtiments RT2005 _FR

8/14/2019 REG2006 méthode réglementaire de calcul thermique des bâtiments RT2005 _FR

http://slidepdf.com/reader/full/reg2006-methode-reglementaire-de-calcul-thermique-des-batiments-rt2005-fr 1/159

Sa-NB 7552

Sa-NB 7552

Pbw~jhk <+>

92(5>(7550



SA-NB 7552++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++9

9+ LÊKÊWIFJSÊ^+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++0

7+ CÊ@JKJSJHK^++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++<

7+9+9 Uwhobs++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++ < 7+9+7 Gçsjmbks+++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++ < 7+9+> hkb +++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++ < 7+9+3 lwhrub++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++ 1 7+9+2 Ni~ uiwsjnrfjbw~ ++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++ 1

7+7+9 Ikkêb++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++ 1 7+7+7 ~nbkiwjh~ cb `hknsjhkkbmbks ++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1

>+ CHKKÊB^ C‚BKSWÊB^+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++1

3+ IWNAJSBNSRWB CB^ NIFNRF^+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++:

2+ NFJMIS+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++95

0+ FB^ ^NBKIWJH^ NHKPBKSJHKKBF^++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++97

<+ NIWINSÊWJ^ISJHK SABWMJYRB CB F‚BKPBFHUUB ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++91

<+2+9 niwinsêwj~sjyrb~ cb~ uiwhj~ huiyrb~ cb naiyrb lwhrub+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 75 <+2+7 niwinsêwj~sjyrb~ cb f‚jkbwsjb cb naiyrb lwhrub++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 79

1+ NIFNRF CB^ CÊGJS^ C,IJW ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++77

1+7+9 jkswhcrnsjhk +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 7> 1+7+7 Pifbrw~ cb~ cêgjs~ å wbuwbkcwb bs å `hrwkjw Ypi~hr ~ubn bs Ypiwbu~ubn +++++++++++++++++++++++++++++++++++++++++++++++++++ 7> 1+7+> pbksjfisjhk mênikjyrb +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 7> 1+7+3 pbksjfisjhk kisrwbffb uiw nhkcrjs~+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 70 1+7+2 pbksjfisjhk azgwjcb +++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 71 1+7+0 ibwisjhk uiw hrpbwsrwb cb~ ̀ bkïswb~ +++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++ 7:

1+>+9 niwinsêwj~isjhk ir kjpbir cr gçsjmbks+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ >5 1+>+7 niwinsêwj~isjhk ir kjpbir cb fi hkb+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ >5 1+>+> ui~~ilb cr gçsjmbks å fi hkb +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++ >9 1+>+3 nifnrf cb~ cêgjs~ c‚ijw å swipbw~ f‚bkpbfhuub++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ >9

1+>+2 Wêuiwsjsjhk cb f‚ijw bkswiks hr ~hwsiks uiw fb~ uiwhj~ bqsêwjbrwb~ uhrw naiyrb lwhrub++++++ ++++++++++++++++++++ >0 1+>+0 Nifnrf cb~ cêgjs~ bkswb lwhrub~++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ >0 :+ BNFIJWILB +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++><

:+9+9 Szub~ cb gçsjmbks~ pj~ê~++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ >< :+9+7 Yrbf ênfijwilb uwbkcwb bk nhmusb 8+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ><



:+>+9 Nifnrf cb fi nhk~hmmisjhk uhrw fb lwhrub++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++ >1 :+>+7 Nifnrf cb fi urj~~iknb jk~siffêb +++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ >1 :+>+> pifbrw~ cr nhb``jnjbks N9+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ >: :+>+3 Nifnrf cr nhb``jnjbks N>3 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ >:

95+ GB^HJK^ C‚BIR NAIRCB ^IKJSIJWB+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++3>

99+ NHMUHWSBMBKS SABWMJYRB C,RK LWHRUB BS NHRUFILB IPBN FB ^Z^SBMBC‚BMJ^^JHK ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++30

99+9+9 Cb~nwjusjhk lfhgifb cr mhcáfb++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 30 99+9+7 nifnrf cb~ sbmuêwisrwb~ bqsêwjbrwb~ êyrjpifbksb~ ? +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++ 3< 99+9+> Nifnrf cb fi nhkcrnsiknb sabwmjyrb crb å fi pbksjfisjhk bs cb α bjby ? +++++++++++++++++++++++++++++++++++++++++++++++++++ 3< 99+9+3 Nifnrf cb~ irswb~ nhkcrnsiknb~ ++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 31 99+9+2 Cêsbwmjkisjhk cb fi sbmuêwisrwb c,ijw bs cb fi sbmuêwisrwb huêwisjpb ? +++++++++++++++++++++++++++++++++++++++++++++++ + 31 99+9+0 Cêsbwmjkisjhk cb fi cêubwcjsjhk nhkpbksjhkkbffb uiw fb~ uiwhj~ bs fb wbkhrpbffbmbks c‚ijw ++++++++++++++++++ 3:

99+7+9 Wizhkkbmbks ~hfijwb lfhgif issbjlkiks rkb uiwhj +++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++ 25 99+7+7 uwj~b bk nhmusb cb~ mi~yrb~ `jqb~++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 29 99+7+> lb~sjhk mikrbffb cb~ uwhsbnsjhk~ ~hfijwb~ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 2> 99+7+3 Nifnrf cb~ `frq ~hfijwb~ bs cb lwikcb fhklrbrw c,hkcb pbw~ fi phrsb nêfb~sb swik~mj~ ir fhnif ++++++++++++ 23

97+ BMJ^^JHK CB NAIFBRW BS CB @WHJC++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++21

97+9+9 Piwjisjhk~ ~uisjifb~+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 2: 97+9+7 Uwênj~jhk cb fi wêlrfisjhk sbwmjkifb !Piwjisjhk~ sbmuhwbffb~* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 05

97+3+9 Uwê~bksisjhk++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 0> 97+3+7 Uwjknjub cr nifnrf uhrw rk êmbssbrw++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 02 97+3+> Iuufjnisjhk ir nifnrf ~rw rkb abrwb ++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 00

97+0+9 Bmbssbrw~ nairc~ +++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++ 0< 97+0+7 êmbssbrw~ `whjc~ ++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++ 0:

97+<+9 Fhnirq c,bkswê~ c,ijw ~ik~ ~z~sámb cb wb`whjcj~~bmbks++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++ 0: 97+<+7 Fhnirq cb swik~`bws bs c,bqswinsjhk +++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++++++++ 0:

9>+ CJ^SWJGRSJHK AZCWIRFJYRB BS CB @FRJCB @WJLHWJLÁKB+++++++++++++++++++++++++++++++++++++++++++++++++<5

9>+9+9 Nifnrf cb fi urj~~iknb khmjkifb bk nairc bs `whjc+++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++ <5 9>+9+7 Ubwsb~ sabwmjyrb~ cb~ wê~birq cb cj~swjgrsjhk ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++ <5 9>+9+> Ubwsb~ cb cj~swjgrsjhk bs nhk~hmmisjhk cb~ irqjfjijwb~ ir kjpbir cj~swjgrsjhk uiw lwhrub bk `hknsjhk cb fi urj~~iknb cbmikcêb cik~ fb lwhrub bs uhrw fb~ jksbwlwhrub~ bs jksbwhkb~++++++++++++++++++++++++++++++++++++++++++++++++++++ <2

9>+>+9 Uhmub~ å naifbrw ~rw ghrnfb c‚bir++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ <: 9>+>+7 Fb~ ~z~sámb~ å cêgjs cb wê`wjlêwiks piwjigfb bs fb~ sabwmh`wjlhuhmub~ +++++++++++++++++++++++++++++++++++++++++++++++ <:

93+ SWIJSBMBKS BS CJ^SWJGRSJHK C,IJW++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++15

93+>+9 Uwjknjub cb uwj~b bk nhmusb++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 19 93+>+7 Nifnrf cb f,jmuins cb~ nhmuh~iks~++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++++++++ 17

93+3+9 Uwjknjub cb uwj~b bk nhmusb++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1< 93+3+7 Nifnrf cb f‚jmuins cb~ nhmuh~iks~+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1<



92+ UBWSB^ CB CJ^SWJGRSJHK CB F‚BIR NAIRCB ^IKJSIJWB ++++++++++++++++++++++++++++++++++++++++++++++++++++:>

90+ UBWSB^ CB ^SHNDILB AHW^ LÊKBWISBRW^ ^SHNDBRW^ ++++++++++++++++++++++++++++++++++++++++++++++++:0

90+9+9 Nair``b bir êfbnswjyrb~ +++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++ :0 90+9+7 irswb~ giffhk~ cb uwhcrnsjhk c‚bir naircb ~ikjsijwb uiw innrmrfisjhk !giffhk~ cb ~shndilb*+++++++++++++ :<

9<+ LÊKÊWISJHK CB NAIFBRW& CB @WHJC BS C‚BN^+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++:1

9<+0+9 Lêkêwisbrw å b``bs Ohrfb +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 957 9<+0+7 Innrmrfisbrw~ LI_++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 957 9<+0+> Lêkêwisbrw å nhmgr~sjhk++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 95> 9<+0+3 Lêkêwisjhk sabwmhczkimjyrb+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 990 9<+0+2 Winnhwcbmbks å rk wê~bir cb naifbrw ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++++++++++++ 97< 9<+0+0 Winnhwcbmbks i rk wê~bir cb `whjc++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 971

91+ JK^SIFFISJHK^ ̂ HFIJWB^ SABWMJYRB^+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++97:

91+3+9 Niusbrw~ ~hfijwb~ +++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++ 9>7 91+3+7 Nair``b-bir ~hfijwb~+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 9>7 91+3+> Giffhk~ cb ~shndilb++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 9>> 91+3+3 Ni~ uiwsjnrfjbw cr ufiknabw ~hfijwb++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 9>>

91+2+9 @hwmrfb lêkêwifb++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 9>3 91+2+7 ni~ c,rk ~z~sámb nhmgjkê !nair``ilb bs BN^*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 9>2 91+2+> Bquwb~~jhk cb~ uiwimáswb~ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 9>2

91+0+9 Nair``b-bir ~hfijwb jkcjpjcrbf+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 9>1 91+0+7 Jk~siffisjhk c,bir naircb ~hfijwb nhffbnsjpb å iuuhjks nbkswifj~ê +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 9>1 91+0+> Jk~siffisjhk c,bir naircb ~hfijwb nhffbnsjpb å iuuhjks~ jkcjpjcrbf~ ++++++++++++++++++++++++++++++++++++++++++++++++++++++ 9>1

91+<+9 Iuuhjks nbkswifj~ê !jk~siffisjhk nhffbnsjpb c,bir naircb ~ikjsijwb*+++++++++++++++++++++++++++++++++++++++++++++++++++++++ 9>: 91+<+7 Iuuhjks jkcjpjcrbf !jk~siffisjhk c,bir naircb ~ikjsijwb*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 9>: 91+<+> Ubwsb~ wênruêwigfb~ cb f‚iuuhjks+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 9>:

9:+ JK^SIFFISJHK ̂ HFIJWB UAHSHPHFSIÈYRB^ +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++939

9:+>+9 Bkbwljb jknjcbksb Aj++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 937 9:+>+7 Urj~~iknb nwïsb U5 +++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++ 933 9:+>+> Jkcjnb cb ubw`hwmiknb Wu+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 932 9:+>+3 Bqbmufb~ +++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++++ 932

75+ NHB@@JNJBKS NBU CR GÇSJMBKS++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++93<

79+ MÊSAHCB SA-B+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++931



79+7+9 Nifnrf ~rw fi ohrwkêb naircb cb wê`êwbknb++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 931 79+7+7 Nhwwbnsjhk uhrw f‚b``bs ~êyrbksjbf ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 931 79+7+> Nifnrf cb S jn ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 931

79+>+9 Sbmuêwisrwb bs azlwhmêswjb++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 93: 79+>+7 Wizhkkbmbks ~hfijwb bs wizhkkbmbks `whjc pbw~ fi phôsb nêfb~sb+++++++++++++++++++++++++++++++++++++++++++++++++++++++ 925 79+>+> Pjsb~~b cr pbks +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 929

79+2+9 Iuuwhnab lêkêwifb++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 929 79+2+7 Nifnrf cr cêgjs c‚ijw cô å f‚hrpbwsrwb cb~ `bkïswb~ bs cb~ hrpwiks~ ~uênj`jyrb~++++++++++++++++++++++++++++++++++ 929 79+2+> nifnrf cb fi ~rw`inb fjgwb bk hrpbwsrwb mikrbffb++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++ 927 79+2+3 Nifnrf cr cêgjs c‚ijw cô å f‚hrpbwsrwb c,hrpwiks~ ~uênj`jyrb~ bk jkhnnruisjhk uhrw fb~ lwhrub~ å r~ilbirswb yrb c‚aigjsisjhk bs k‚i~~rwiks ui~ f‚aêgbwlbmbks +++++++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++++ 92> 79+2+2 ^rwpbksjfisjhk uhrw fb nhk`hws c,êsê++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 92>

79+<+9 Wê`êwbknb~ wêlfbmbksijwb~ bs khwmisjpb~ å rsjfj~bw +++++++++++++++++++++++++++++++++++++++++++++++++++ +++++++++++++++++++++++++ 923 79+<+7 Niwinsêwj~isjhk cr ~jsb ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 923 79+<+> Niwinsêwj~isjhk cr lwhrub+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 923

IKKBQB I NIFNRF CB^ URJ^^IKNB^ MHZBKKB^ CB PBKSJFISBRW^ +++++++++++++++++++++++++++++++++920

I+7+9 GÇSJMBKS^ IRSWB^ YRB C‚AIGJSISJHK +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++920

I+7+7 GÇSJMBKS^ C‚AIGJSISJHK NHFFBNSJ@^ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++92<

I+7+> MIJ^HK^ JKCJPJCRBFFB^+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++92<

IKKBQB G NIFNRF CB^ ^Z^SÁMB^ C‚ÊMJ^^JHK NHMUH^JSB+++++++++++++++++++++++++++++++++++++++++++++++++921



9+ LÊKÊWIFJSÊ^

9+9 HGOBS CR CHNRMBKS

9+7 NIFNRF CR NHB@@JNBKS Nbu BS CR NHB@@JNJBKS NbuWB@

9+> UWÊNJ^JHK



7+ CÊ@JKJSJHK^

7+9 CÊ@JKJSJHK^ RSJFB^ UHRW FI ^BLMBKSISJHK CB^ NIFNRF^

7+9+9 UWHOBS

‧

‧

‧

7+9+7 GÇSJMBKS

7+9+> _HKB



3+ IWNAJSBNSRWB CB^ NIFNRF^

@jlrwb 9 ? Iwnajsbnsrwb cb~ nifnrf~ uhrw rk gçsjmbks



2+ NFJMIS

2+9 PIFBRW^ CB WÊ@ÊWBKNB IR KJPBIR CB FI MBW

k kf f k w j a ` `



α

α

2+7 NHWWBNSJHK C‚IFSJSRCB

α

Sigfbir 7 ? nhwwbnsjhk cb sbmuêwisrwb



0+ FB^ ^NBKIWJH^ NHKPBKSJHKKBF^

0+9 LÊKÊWIFJSÊ^ BS SZUB C‚R^ILB^

Szub~ c‚r~ilb

Sigfbir > ? Szub~ cb hkb~



Kjpbir cbsbmuêwisrwb

HnnruisjhkWêcrnsjhk cb nair`ìlb cb

mhjk~ cb 31aWêcrnsjhk cb nair`ìlb

cb ufr~ cb 31a

Sigfbir 0 ? Sbmuêwisrwb~ cb nhk~jlkb nhkpbksjhkkbffb~ bk nair`ìlb

Hnnruisjhk bkfhlbmbks~

Hnnruisjhkirswb~ ni~

Wêcrnsjhk cbwb`whjcj~~bmbks cb mhjk~

cb 31a

Wêcrnsjhk cbwb`whjcj~~bmbks cb ufr~

cb 31 a

71µN 70 µN >5µN >5 µN

Sigfbir < ? Sbmuêwisrwb~ cb nhk~jlkb nhkpbksjhkkbffb~ bk wb`whjcj~~bmbks

Mhj~ Khmgwb cb ohrw~ cb piniknb~ k o&pin

Sigfbir 1 ? Uêwjhcb~ cb piniknb~ uhrw f‚r~ilb bk~bjlkbmbks

Ahwijwb~ c,hnnruisjhk Abrwb~ uiw ohrw Ohrw~ uiw ~bmijkb

Sigfbir : ? ~nêkiwjh~ c,rsjfj~isjhk cb fi pbksjfisjhk

Ahwijwb c,hnnruisjhk Abrwb~ uiw ohrw Ohrw~ uiw ~bmijkb

Sigfbir 95 ? ~nêkiwjh~ c,rsjfj~isjhk cb f,ênfijwilb iwsj`jnjbf



0+> IUUHWS^ JKSBWKB^

Szub~ c‚r~ilb~ Ahwijwb~ cbmijksjbk bksbmuêwisrwb

\(m· bkhnnruisjhk dl(a(m· bkhnnruisjhk

Sigfbir 99 ? Pifbrw~ nhwwb~uhkciks irq cj``êwbks~ r~ilb~ cb~ hkb~

Sigfbir 97 ? Wêuiwsjsjhk cb~ iuuhws~ ~bk~jgfb~



0+3 CÊ@JKJSJHK CB FI UÊWJHCB CB NAIR@@B BS CB WB@WHJCJ^^BMBKS

Lwhr b 9

Lwhr b 7



Wbmiwyrb ?

_hkb 9

_hkb 7

Gçsjmbks



‧

‧

∙=khwjbksisjh

gijb I I

! *

∙∙ ⋂

=

khwjbksisjh

gijb

khwjbksisjh

gijb~u|gijb

~u| I

^ I

^ X X

X

! *

∙∙ ⋂

=

khwjbksisjh

gijb

khwjbksisjh

gijbfgijb

f I

S I

S X 9

9

Sigfbir 9> ? niwinsêwj~sjyrb~ cb~ gijb~ ~ik~ uwhsbnsjhk ~hfijwb mhgjfb wblwhruêb~ uiw hwjbksisjhk

bs uiw mi~yrb uwhnab

∙=khwjbksisjh

gijb I I

! *

∙∙ ⋂

=

khwjbksisjh

gijb

khwjbksisjh

gijbiu|gijb

iu| I

^ I

^ X X

X

! *

∙∙ ⋂

=

khwjbksisjh

gijb

khwjbksisjh

gijbfgijb

f I

S I

S X 7

7

Sigfbir 93 ? niwinsêwj~sjyrb cb~ gijb~ ipbn uwhsbnsjhk~ ~hfijwb~ mhgjfb~ wblwhruêb~ uiw

hwjbksisjhk bs uiw mi~yrb uwhnab



<+3 PIFBRW^ NHKPBKSJHKKBFFB^

Sigfbir 92 ? pifbrw~ nhkpbksjhkkbffb~

<+2 UI^^ILB CB^ NIWINSÊWJ^SJYRB^ CB F‚BKPBFHUUB CR GÇSJMBKS Å FI _HKBURJ^ IR LWHRUB+

<+2+9 NIWINSÊWJ^SJYRB^ CB^ UIWHJ^ HUIYRB^ CB NAIYRB LWHRUB

I_b =∙ JubqsXlw Ilw !By 9*

Igçsb = ∙I_b !By 7*

gçsb

_b

_ I

I I u = X !By >*

gçsb

lw lw ubqs

lw I

I J I u

⋂= X X !By 3*

∙ ∙∗∗=lw khwjbksisjh

gijbhuagis S hupgis I I I I X X !By 2*

hugis

lw khwjbksisjh

gijbgijbS

hugis I

IR IRgis

R X

X

∙ ∙⋂∗⋂

= !By 0*



!By <*

Sigfbir 90 ? wêuiwsjsjhk cb~ niwinsêwj~sjyrb~ cb~ uiwhj~ huiyrb~

<+2+7 NIWINSÊWJ^SJYRB^ CB F‚JKBWSJB CB NAIYRB LWHRUB



1+ NIFNRF CB^ CÊGJS^ C,IJW

‧

‧

‧

‧

1+9 NIWINSÊWJ^ISJHK CR LWHRUB BS WÁLFB CB ̂ BLMBKSISJHK

‧

‧

‧

∙ ∙;bkswêblwhrub~c bkswêblwhrub~c

wbulw ~hrlw YpiYpi, ,

-

-

~bk~ cb~ nifnrf~

@jlrwb > ? ~bk~ cb~ nifnrf~



1+7 NIFNRF CB^ CÊGJS^ ÛÊNJ@JYRB^

1+7+9 JKSWHCRNSJHK

1+7+7 PIFBRW^ CB^ CÊGJS^ Å WBUWBKCWB BS Å @HRWKJW YPI^HRÛBN BS YPIWBUÛBN

1+7+> PBKSJFISJHK MÊNIKJYRB

‧

‧

Ypi~hrhnn = Ncbu N`wb~ Ypi~hr~ubnhnn !By 1*

Ypi~hrjkhnn = Ncbu N`wb~ Ypi~hr~ubnjkhnn !By :*

Ypiwbuhnn = Ncbu N`wb~ Ypiwbu~ubnhnn !By 95*

Ypiwbujkhnn = Ncbu N`wb~ Ypiwbu~ubnjkhnn !By 99*1+7+>+9 ^bnsbrw wê~jcbksjbf

Crwêb c‚rsjfj~isjhk bk lwikc cêgjs !Crlc*!bk a(~bmijkb*

Sigfbir 9< ? Crwêb~ c,rsjfj~isjhk Crlc bk lwikc cêgjs bk ~bnsbrw wê~jcbksjbf



Ypiwbu~ubn = !Yuhjksbwbu / Crlc $ Ygi~bwbu / !901 „ Crlc * * ( 901 !By 97*

Ypi~hr~ubn = !Yuhjksb~hr / Crlc $ Ygi~b~hr / !901 „ Crlc * * ( 901 !By 9>*

Sigfbir 9<

1+7+>+7 Khk wê~jcbksjbf

Ypikhm~hr&Ypikhmwbu&

Nhb``jnjbks cb wêcrnsjhk cb~ cêgjs~

!Nwcgkw*

Sigfbir 91 ? Nhb``jnjbks~ cb wêcrnsjhk cb~ cêgjs~ bk khk wê~jcbksjbf Nwcgkw

Ypiwbu~ubnhnn = Nwcgkw Ypikhmwbuhnn !By 93*

Ypiwbu~ubnjkhn = Ypikhmwbujkhn !By 92*

Ypi~hr~ubnhnn = Nwcgkw Ypikhm~hrhnn !By 90*

Ypi~hr~ubnjkhn = Ypikhm~hrjkhn !By 9<*



1+7+>+> Nhb``jnjbks~ cb cêui~~bmbks Ncbu

Pifbrw uiw cê`irs

Nhmuh~iks~ irshwêlfigfb~ nbwsj`jê~

Sigfbir 9: ? Pifbrw~ cb Ncbu uhrw fi pbksjfisjhk mênikjyrb

1+7+>+3 Nhb``jnjbks cb ̀ rjsb cb~ wê~birq N`wb~

Nfi~~b cb Nf`wb~

Pifbrw cb N`wb~

Sigfbir 75 ? Pifbrw cb N`wb~ bk `hknsjhk cb fi nfi~~b Nf`wb~

Szub cb wê~bir

Nfi~~b c,êsiknaêjsê

cr wb~bir

Dwb~

!m>

(!~+m7

* ~hr~ 9 Ui*!uhrw mêmhjwb*

Nfi~~b Nf`wb~w

Sigfbir 79 ? nfi~~b~ cb Nf`wb~ uhrw fi pbksjfisjhk mênikjyrb



1+7+3 PBKSJFISJHK KISRWBFFB UIW NHKCRJS^

∀

∀

∀

∀

ό

Sigfbir 9<

ω

∀

∀ δ ω δ

∀ όnhrcb ω

∀



-

-

∀

∀ ω

∀ ∀

∀ ω

∀ ∀∀

∀ ∀

∀

∀ ω

∀ ∀ ∀ ∀ ∀



ω

∀ u bqsw

∀ u nhkc

Sb Sj

∀ u nhrcb

∀ u ghrnab

@jlrwb 3 ? ^naêmi cb uwjknjub uhrw fb nifnrf cb ∀umhs

1+7+2 PBKSJFISJHK AZGWJCB

Sigfbir 77 ? ahwijwb~ c,rsjfj~isjhk cr lwikc cêgjs nrj~jkb bk pbksjfisjhk~ azgwjcb



Ypiwbu~ubn = !Yuhjksb / Crlca $ Ygi~b / !901 „ Crlca * * ( 901 !By 71*

Crwêb c‚rsjfj~isjhk bk lwikc cêgjs !Crlca*!bk a(~bmijkb*

Sigfbir 7> ? Crwêb~ c,rsjfj~isjhk uiw cê`irs !Crlca* bk lwikc cêgjsbk ~bnsbrw wê~jcbksjbf bs bk pbksjfisjhk azgwjcb

1+7+0 IBWISJHK UIW HRPBWSRWB CB^ @BKÏSWB^

1+7+0+9 Khk wê~jcbksjbf

Yp`bk~hrhnn = N`bkg ! Ypikhm~hrnhnn $ Ypikhmwbuhnn* !By 7:*

Yp`bk~hrjkhnn = N`bkg ! Ypikhm~hrjkhnn $ Ypikhmwbujkhnn * !By >5*

Yp`bkwbuhnn = Yp`bk~hrhnn !By >9*

Yp`bkwbujkhnn = Yp`bk~hrjkhnn !By >7*



1+> NIFNRF CB^ CÊGJS BNAIKLÊ^ IR SWIPBW^ CB F,BKPBFHUUB CB FI _HKB BSBKSWB LWHRUB^

1+>+9 NIWINSÊWJÎSJHK IR KJPBIR CR GÇSJMBKS

‧

‧

‧

Sigfbir 73

R~ilb Ubwmêigjfjsê uiw cêìrs !bk m> (!a+m7**

Gçsjmbks or~sj`jê cik~fb nicwb cb fi

cêmiwnab cb yrifjsê cbf‚êsiknaêjsê å f‚ijw

Sigfbir 73 ? Pifbrw~ uiw cêìrs cb fi ubwmêigjfjsê cb~ uiwhj~ bqsêwjbrwb~

1+>+7 NIWINSÊWJÎSJHK IR KJPBIR CB FI _HKB

‧

‧



1+>+3+7+7 Cêsbwmjkisjhk cr khmgwb cb nhmuh~iks~ bs cb fbrw uh~jsjhk

‧ Fb~ cêìrs~ c‚êsiknaêjsê

Wêuiwsjsjhk cb fi

ubwmêigjfjsê å f‚ijw

@iìicb ir pbks @iìicb~ fisêwifb~ @iìicb ~hr~ fb pbks

Sigfbir 70 ? Wêuiwsjsjhk cb~ cêìrs~ c,êsiknaêjsê uhrw fb~ hkb~ ubwmêigfb~ahwjhksifbmbks

Wêuiwsjsjhk cb fi ubwmêigjfjsê å f‚ijw Uiws cb fi ̀ iìicb cjsb¤ ir pbks ´

Uiws cb fi ììicb cjsb¤ ~hr~ fb pbks ´

Sigfbir 7< ? Wêuiwsjsjhk cb~ cêìrs~ c,êsiknaêjsê uhrw fb~ hkb~ khk ubwmêigfb~ahwjhksifbmbks

‧ Fb~ bkswêb~ c‚ijw



Wêuiwsjsjhk cb~ bkswêb~ c‚ijw @iìicb ir pbks @iìicb~ fisêwifb~ @iìicb ~hr~ fb pbks

Sigfbir 71 ? Wêuiwsjsjhk cb~ bkswêb~ c,ijw uhrw fb~ hkb~ ubwmêigfb~ ahwjhksifbmbks bs

khk ubwmêigfb pbwsjnifbmbks

Wêuiwsjsjhk cb~ bkswêb~ c‚ijw Uiws cb fi ììicb cjsb ¤ irpbks ´

Uiws cb fi ììicbcjsb ¤ ~hr~ fb pbks ´

Sigfbir 7: ? Wêuiwsjsjhk cb~ bkswêb~ c,ijw uhrw fb~ hkb~ khk ubwmêigfb~ahwjhksifbmbks bs khk ubwmêigfb~ pbwsjnifbmbks

Wêuiwsjsjhk cb~ bkswêb~c‚ijw

@iìicb ir pbks @iìicb~ fisêwifb~ @iìicb ~hr~ fb pbks

Sigfbir >5 ? Wêuiwsjsjhk cb~ bkswêb~ c,ijw uhrw fb~ hkb~ ubwmêigfb~ pbwsjnifbmbks

1+>+3+7+> Nifnrf cb fi uwb~~jhk ~rw fb~ ììicb~ uhrw rk nhmuh~iks

Airsbrw cr gçsjmbks

Nu ììicb ir pbks

Nu ììicb~ fisêwifb~

Nu ììicb ~hr~ fb pbks

$ 5&72 -5+2 - 5&2

$ 5&32 -5+2 - 5&2

$ 5&05 -5+2 - 5&2

Sigfbir >9 ? Nu uhrw fb~ hkb~ ubwmêigfb~ ahwjhksifbmbks



Nu ììicb cjsb ¤ ir pbks ´

Nu ììicb cjsb ¤ ~hr~ fb pbks ´

Sigfbir >7 ? Nu uhrw fb~ hkb~ khk ubwmêigfb~ ahwjhksifbmbks

Ubqs&nhmu = ωi + !5+2 + Nu + !5+: pb*7 - anhmu + !!αj „ αbj * + l ( αb&wb` ** !By >3*

ω

α

∀u = Ubqs&nhmu - ujg !By >2*

1+>+3+7+3 Nifnrf cb~ cêgjs~ ir swipbw~ cb~ cêìrs~ c‚êsiknaêjsê

^j ∀u 6 5 ypcb` = - yp3Ui !-∀u(3*7(>

ymcb` = ypcb` /ωj (>055

^j ∀u ≢ 5 ypcb` = yp3Ui !∀u(3*7(>

ymcb` = ypcb` /ωb (>055

!By >0 *

∀ω αω α

1+>+3+7+2 Nifnrf cb~ cêgjs~ ir swipbw~ cb~ bkswêb~ c‚ijw

∀



Uhrw ∀u ≣ 5 Ui ? ypbi = -9&9+Mbi+!-∀u(75*

5&2

ymbi = ypbi /ωj5&2/ωi

5&2 (>055

Uhrw 5 Ui 6 ∀u ≣ 75 Ui ? ypbi = 9&9+Mbi+!∀u(75*5&2

ymbi = ypbi /ωb5&2/ωi

5&2 (>055

Uhrw ∀u ; 75 Ui ? ypbi = 5&22+Mbi+∀u(15 $ <<+Mbi (15


5&2 (>055

!By >< *

Uhrw ∀u ≣ 5 Ui ? ypbi = -9&9+Mbi+!-∀u(75*5&2

ymbi = ypbi /ωj5&2/ωi 5&2 (>055

Uhrw ∀u ; 5 Ui ? ypbi = 9&9+Mbi+!∀u(75*5&2


5&2 (>055

!By >1*

1+>+3+7+0 Cêgjs~ ~rw f‚bk~bmgfb cb fi hkb

∙ ymcb`

∙ ymbi

1+>+3+> nifnrf cb Ujg

Ymcb` !ujg* $ Ymbi!ujg* $ YmiS~hr $YmiSwbu $ YmiSnhkc= 5 !By >:*



:+ BNFIJWILB

:+9 CHMIJKB C‚IUUFJNISJHK

:+9+9 S ZUB^ CB GÇSJMBKS^ PJ^Ê^

:+9+7 YRBF ÊNFIJWILB UWBKCWB BK NHMUSB 8

:+7 NIFNRF CB FI NHK^HMMISJHK C‚BKBWLJB UHRW F‚ÊNFIJWILB CR GÇSJMBKS

NBNFXa = ή NBNFXhkb !By 3>*

NBNFXhkb = ή NBNFXLW !By 33*

NBNF NBNFXa+



:+> MÊSAHCB CB NIFNRF BK KHK WÊ^JCBKSJBF

:+>+9 NIFNRF CB FI NHK^HMMISJHK UHRW FB LWHRUB

Sigfbir >> ? uiwimáswb~ kênb~~ijwb~ ir nifnrf cb fi nhk~hmmisjhk crb å f‚ênfijwilbiwsj`jnjbf

NBNFXLW = ή NBNFXfhnif !By 32*

NBNF XfhnifX = Ubnf+/ UXIbnf / Ilw / N9 / N>3 !By 30*

UXIbnf Ifhnif ( Ilw !By 3<*

:+>+7 NIFNRF CB FI URJ^^IKNB JK^SIFFÊB



Pifbrw uiw cê`irs

:+>+> PIFBRW^ CR NHB@@JNJBKS N9

Sigfbir >3 ? pifbrw~ cr nhb``jnjbks N9

:+>+3 NIFNRF CR NHB@@JNJBKS N>3

:+>+3+9 Cêsbwmjkisjhk cb f‚inná~ å f‚ênfijwilb kisrwbf c‚rk fhnif

‧≣

‧

‧



:+>+3+> Nifnrf cb N>3

@jlrwb 2 ? êphfrsjhk cb N>3 bk `hknsjhk cb f‚ênfijwilb kisrwbf

Sigfbir >2 ? pifbrw~ cb Bjkiswb` bs cb N>3wb`



:+3 MÊSAHCB CB NIFNRF BK WÊ^JCBKSJBF

:+2 NIFNRF CB^ IUUHWS^ WÊNRUÊWIGFB^ CÔ^ Å F‚ÊNFIJWILB

@bnfN = 5+2 NBNFXLW !By 2>*

@bnfW = 5+2 NBNFXLW !By 23*

@bnfN @bnfW



95+ GB^HJK^ C‚BIR NAIRCB ^IKJSIJWB

! * BN^n|r|r|||| Wis P nY /+++ α α ω ∗=

ω ω|

n n |

P

α

α n|

Wis BN^



Szub c‚r~ilb~ i Kr

Mij~hk~ jkcjpjcrbffb~

= !3<5+: fk !Kr* „ 95<2* ( Kr

~j Kr ; 7< m·

= 9<+< ~jkhk

m7 cb ~rwìnb aigjsigfb

Fhlbmbks~ nhffbnsj`~

= !3<5+: fk !KrXfls* „ 95<2* (

KrXfls~j KrXfls ≢ 7< m·

= 9<+< ~jkhk

Ipbn KrXfls = Kr(kgwbXfls

m· cb ~rwìnb aigjsigfb shsifb

Aêgbwlbmbks >>5 Khmgwb cb fjs~

Êsigfj~~bmbks ~ikjsijwb ~ik~ aêgbwlbmbks 975 Khmgwb cb fjs~

Êsigfj~~bmbks ~ikjsijwb ipbn aêgbwlbmbks -ipbn Gfiknaj~~bwjb+

9525 Khmgwb cb fjs~

Êsigfj~~bmbks ~ikjsijwb ipbn aêgbwlbmbks -~ik~ Gfiknaj~~bwjb+

002 Khmgwb cb fjs~

Bk~bjlkbmbks

Grwbirq

îffb~ cb ~ubnsinfb~ cb nhk`êwbknb~

Nhmmbwnb~

Gb~hjk~ c‚bir naircbkhk uwj~ bk nhmusb

Wb~sirwisjhk 7 wbui~ uiw ohrw+ Nrj~jkbswicjsjhkkbffb

722 Khmgwb cb wbui~ uiw ~bwpjnb

Wb~sirwisjhk 7 wbui~ uiw ohrw+ ^bf` :2 Khmgwb cb wbui~ uiw ~bwpjnb

Wb~sirwisjhk 9 wbui~ uiw ohrw+ Nrj~jkbswicjsjhkkbffb

972 Khmgwb cb wbui~ uiw ~bwpjnb

Wb~sirwisjhk 9 wbui~ uiw ohrw+ ^bf` 32 Khmgwb cb wbui~ uiw ~bwpjnb

Aósbf - 9/ - ~ik~ Gfiknaj~~bwjb 002 Khmgwb cb naimgwb~

Aósbf - 9/ - ipbn Gfiknaj~~bwjb 1>5 Khmgwb cb naimgwb~

Aósbf - 7/ - ~ik~ Gfiknaj~~bwjb :95 Khmgwb cb naimgwb~

Aósbf - 7/ - ipbn Gfiknaj~~bwjb 95<2 Khmgwb cb naimgwb~

Aósbf - >/ - ~ik~ Gfiknaj~~bwjb 9905 Khmgwb cb naimgwb~

Aósbf - >/ - ipbn Gfiknaj~~bwjb 9>72 Khmgwb cb naimgwb~

Aósbf - 3/ bs LN - ~ik~ Gfiknaj~~bwjb 9352 Khmgwb cb naimgwb~

Aósbf - 3/ bs LN - ipbn Gfiknaj~~bwjb 92<5 Khmgwb cb naimgwb~

Êsigfj~~bmbks ~uhwsj` 9755 Khmgwb cb chrnab~ jk~siffêb~

^shndilb

Jkcr~swjb

Swik~uhws

Irswb

Gb~hjk~ c‚bir naircbkhk uwj~ bk nhmusb

Sigfbir >0 ? Gb~hjk~ rkjsijwb~ abgchmicijwb~ c‚bir naircb ~ikjsijwb å 35 µN



Wb~sirwisjhk nrj~jkbswicjsjhkkbffb bs ~bf`

Uêwjhcb

Fhlbmbks &

êsigfj~ks~

~ikjsijwbbs c‚aêgbwlbmbks

Bsigfj~ks ~ikjsijwb

~ik~aêgbwlbmbks 9 wbui~ uiw ohrw

7 wbui~ uiw ohrw

Aósbffbwjb Bsigfj~ks

~uhwsj`

Cb < å 1 a 5571 553>Cb 1 å : a 557: 552 5 557: 5Cb : å 95 a 5 5 551 553 5 552Cb 95 å 99 a 5 5 5 5Cb 99 å 97 a 552 5 5 552Cb 97 å 9> a 5 5 5 5Cb 9> å 93 a 552 597 550 5Cb 93 å 92 a 5 5 5Cb 92 å 90 a 5 5 552Cb 90 å 9< a 5 553 5

Cb 9< å 91 a 552 550 552Cb 91 å 9: a 557: 553>Cb 9: å 75 a 5 5593Cb 75 å 79 a 5571 5Cb 79 å 77 a 557: 5Cb 77 å 7> a 5 5593

Ohrw~ uiw ~bmijkb~

<2 !cr frkcj ir

pbkcwbcj*2 !cr frkcj ir pbkcwbcj* <

2 !cr frkcj irpbkcwbcj*

Sigfbir >< ? nhb``jnjbks~ ahwijwb~ cb ~hrsjwilb bs cb wêuiwsjsjhk cb~ yriksjsê~nhk~hmmêb~



99+ NHMUHWSBMBKS SABWMJYRB C,RK LWHRUB BS NHRUFILB IPBN FB^Z^SBMB C‚BMJ^^JHK

99+9 MHCÁFB SABWMJYRB

99+9+9 CB^NWJUSJHK LFHGIFB CR MHCÁFB

@jlrwb 0 ? ^naêmi cr mhcáfb cb gçsjmbks

α

α

α

α

α

α



*o `l o opi o | A S |N N a ⋂$⋂⋂$=

∙

∙ ⋂

= o

oYmi

Ymia

a

o

o o

by

α α

ή ή

! *bypi

by`lby

bjby NN

Aa

ϊ⋂$

ϊ⋂∗

=α

99+9+3 NIFNRF CB^ IRSWB^ NHKCRNSIKNB^

Alj~ = Islwhrub ( ! 9(anj - 9(aj~ *

Alb~ =|

9d =ή Id Rd

Alm~ = aj~ Im

Albm = 9( !9(ASa - 9(Alm~*

ASa = IgisXhu/RgisXhu

99+9+2 CÊSBWMJKISJHK CB FI SBMUÊWISRWB C,IJW BS CB FI SBMUÊWISRWB HUÊWISJPB ?

α α



α α

αm&s = Tαm&s-9 ! Nm ( >&0 - 5+2 !R>$Albm* * $ Πmshs] ( TNm ( >&0 $ 5+2 !R>$Albm*]

αm = !αm&s $ α m&s-9* ( 7

α~ = T Alm~ αm $ Π~ $ Alb~ αb~ $ R9 !αbjby $ Πj ( Albj *] ( ! Alm~ $ Alb~ $ R9 *

αj = TAlj~ α~ $ Albj αbjby $ Πj ] ( !Alj~ $ Albj *

αhu = Ushu+ α~ $ !9-Ushu* αj

Πmshs = Πm $ Albm αbm $R> TΠ~ $ Alb~ αb~ $R9 ! Πj ( Albj $αbjby*] ( R7

99+9+0 CÊSBWMJKISJHK CB FI CÊUBWCJSJHK NHKPBKSJHKKBFFB UIW FB^ UIWHJ^ BS FBWBKHRPBFFBMBKS C‚IJW



99+7 NIFNRF^ CB^ WIZHKKBMBKS^ ^HFIJWB BS CB LWIKCB FHKLRBRW C,HKCBJKNJCBKS^ BS CB^ @FRQ SWIK^MJ^

99+7+9 WIZHKKBMBKS ^HFIJWB LFHGIF ISSBJLKIKS RKB UIWHJ

J~w = @`Cjw+Cwu $ @`Cj``+C`u $ Wwu

99+7+9+9 Wizhkkbmbks ~hfijwb ~rw rkb uiwhj krb

γ υ υ

υ

ξ γ γ

ρ γ γ ξα υ ξ η ρ∗ι ξ η

Cwu = nh~α + JCk



99+7+9+7 Nifnrf cr wizhkkbmbks ~hfijwb cj``r~

!By <:* C`u = Jcj+5&2 !9$nh~η*

99+7+9+> Nifnrf cr wizhkkbmbks ~hfijwb wê`fênaj uiw fb ~hf

!By 15* Wwu = !JCa $ Jcj*+ifg+5&2 !9-nh~η* ipbn ? JCa = JCk/~jkξ bs ifg = 5&7

ι

ηγξραΠ ρ∗ι

99+7+7 UWJ^B BK NHMUSB CB^ MI^YRB^ @JQB^

99+7+7+9 Kisrwb cb~ mi~yrb~

‧

‧



99+7+7+7 Mi~yrb uwhnab ahwjhksif ?

@jlrwb < ? mi~yrb uwhnab ahwjhksif

Π ρ∗ι

Π ξ

Π ξξ Π*

!By 19 * ` a = Mjk T Miq !5 4 T9- !ca-cau*(au]* 4 9]

α

α

!By 17 * @`Cj`` = αl (:5



99+7+7+> Mi~yrb fhjksijk cb szub ufik pbwsjnif ?

@jlrwb 1 ? Ufik pbwsjnif êfhjlkê

ξ Π

99+7+7+3 @insbrw c,i``ijgfj~~bmbks lfhgif cr wizhkkbmbks cjwbns

!By 13* @`Cjw = ` B+ ` a

η

99+7+> LB^SJHK MIKRBFFB CB^ UWHSBNSJHK^ ^HFIJWB^



!By 12* Ufjk = mjk !5+2 4 95-> J~w *

99+7+3 NIFNRF CB^ @FRQ ^HFIJWB^ BS CB LWIKCB FHKLRBRW C,HKCB PBW^ FI PHRSB NÊFB^SBSWIK^MJ^ IR FHNIF

99+7+3+9 Cê`jkjsjhk~ bs khmbknfisrwb



99+> @FRQ SWIK^MJ^ IRQ KŗRC^ CB SBMUÊWISRWB^ ?

Π Π

Π

Π

α

α



99+3 NHRUFILB CR LWHRUB IPBN FB ^Z^SÁMB C‚ÊMJ^^JHK

α

α

α α α

α

α

α

α α α

α α α



97+ BMJ^^JHK CB NAIFBRW BS CB @WHJC

97+9 PIWJISJHK^ ^UISJIFB BS SBMUHWBFFB CB FI SBMUÊWISRWB CB NHK^JLKB

α

α α γα γα

α

α α γα γα

α

α

γα

γα

γα

γα

α α α α



97+9+7 UWÊNJ^JHK CB FI WÊLRFISJHK SBWMJKIFB !PIWJISJHK^ SBMUHWBFFB^*

97+9+7+9 Niwinsêwj~isjhk cb~ uwhcrjs~

Khwmb iuufjnigfb Nbwsj`jnisjhk Nhmmbksijwb



Uwênj~jhk cb fi wêlrfisjhkNhrufb wêlrfisbrw(êmbssbrw

Sigfbir 39 ? Uwênj~jhk cb~ nhrufb~ wêlrfisbrw(êmbssbrw



97+7 UWHLWIMMISJHK

Sigfbir 37 ? Crwêb~ cb wbfiknb bk nair``ilb

Sigfbir 3> ? Crwêb~ cb wbfiknb bk wb`whjcj~~bmbks

97+> NHK^HMMISJHK^ BS IUUHWS^ JKSBWKB^ CR^ IRQ ÊMBSSBRW^ FHNIRQ



Szub cb lb~sjhk pbksjfisbrw fhnif

Sigfbir 33 ? @insbrw cb lb~sjhk cr `hknsjhkkbmbks cb~ pbksjfisbrw~ fhnirq fjê~ ir nair``ilb

Szub cb lb~sjhk pbksjfisbrw fhnif

Sigfbir 32 ? @insbrw cb lb~sjhk cr `hknsjhkkbmbks cb~ pbksjfisbrw~ fhnirq fjê~ ir wb`whjcj~~bmbks

97+3 NIFNRF CB^ CÊGJS^ FHNIRQ BS CR GJFIK AZCWJYRB

97+3+9 UWÊ^BKSISJHK



!By :1 * YmwbnjwnGiss = U~bk~wb` Wby ( !Nui / !Sj „ Sgiss**

Bk mhcb wb`whjcj~~bmbks

Sigfbir 30 ? szuhfhljb uhrw fi wêlrfisjhk cb fi sbmuêwisrwb cb gissbwjb `whjcb

‧

‧



Bk mhcb nair``ilb

97+3+7 UWJKNJUB CR NIFNRF UHRW RK ÊMBSSBRW



97+3+> IUUFJNISJHK IR NIFNRF ^RW RKB ABRWB

‧

‧

‧

97+2 UBWSB^ IR CH^ CB^ ÊMBSSBRW^ JKSÊLWÊ^ IRQ UIWHJ^



‧

‧

‧

j5

j g

W R+ g

9W

+955Q∗

= !By 997*

g

j

b

j

g

WR

W Q

∗=

9+955

97+0 ^Z^SÁMB^ NHMUH^JSB^ BS MRFSJUFB^

97+0+9 BMBSSBRW^ NAIRC^



Sigfbir 3<



97+0+7 ÊMBSSBRW^ @WHJC^

97+< UWJ^B BK NHMUSB CB^ FHNIRQ ^IK^ ÊMBSSBRW CB WB@WHJCJ^^BMBKS

97+<+9 FHNIRQ C,BKSWÊ^ C,IJW ^IK^ ^Z^SÁMB CB WB@WHJCJ^^BMBKS

97+<+7 FHNIRQ CB SWIK^@BWS BS C,BQSWINSJHK



9>+ CJ^SWJGRSJHK AZCWIRFJYRB BS CB @FRJCB @WJLHWJLÁKB

9>+9 UBWSB^ BS NHK^HMMISJHK^ CB CJ^SWJGRSJHK UHRW FB^ WÊ^BIRQAZCWIRFJYRB^

9>+9+9 NIFNRF CB FI URJ^^IKNB KHMJKIFB BK NAIRC BS @WHJC

Urj~~iknb khmjkifb bk nairc ? Ukn

α α T ]

α

Urj~~iknb khmjkifb bk `whjc ? Uk`

α

α

9>+9+7 UBWSB^ SABWMJYRB^ CB^ WÊ^BIRQ CB CJ^SWJGRSJHK

9>+9+7+9 Cj~swjgrsjhk cb lwhrub

‧

‧

‧



Szub cb wê~bircb cj~swjgrsjhk

Iwb~bk

wê~jcbksjbf

Iwb~bk fhnirq cb lwikc

phfrmb ipbn gissbwjbsbwmjkifb cbwênair`ìlb

Iwb~bk fhnirq

irswb~@nhs

Sigfbir 31 ? Szuhfhljb cb wê~bir bk mhcb nair`ìlb

Szub cb wê~bir

cb cj~swjgrsjhk

Iwb~bk

wê~jcbksjbf

Iwb~bk fhnirq cb lwikc

phfrmb ipbn gissbwjbsbwmjkifb uhrw fbwb`whjcj~~bmbks

Iwb~bk fhnirq

irswb~@nhs

Sigfbir 3: ? Szuhfhljb cb wê~bir bk mhcb wb`whjcj~~bmbks

Sbmuêwisrwb cbcj~swjgrsjhk cb nair`ìlb

S cb cjmbk~jhkkbmbks∀S khm γαcjm ^rwu

Sigfbir 25 ? sbmuêwisrwb~ cb cj~swjgrsjhk cb nair`ìlb

Sbmuêwisrwb cbcj~swjgrsjhk cb `whjc

S cb cjmbk~jhkkbmbks ∀S khm γαcjm ^rwu

Sigfbir 29 ? sbmuêwisrwb~ cb cj~swjgrsjhk bk `whjc

‧

‧

‧



∀

∀ ∀

Sigfbir 2> ?

⎘⎘

⎥

⎛

⎖⎖

⎝

⎔ ⎘ ⎥

⎛⎖⎝

⎔ $=

2+5

nhsIlcj~bm

//2 KgK

KgK @ Fbm

! * Kglcj~bm Kglcj~bmypU bmkhmnjwnbm Ü∀= 0<0+5bmkhm (/U/33+04>5miq!

cjm+90>9*!

γα

wisbmUnairc yp kn

bmpkhm=

cjm+90>9*!

γα

wisbmU `whjc yp

k`

bmkhm =

γα



9>+9+7+7 Cj~swjgrsjhk jksbw-lwhrub~ bs jksbw-hkb~

ή

! ή *

ή

T ]

ή ή ∀

ή ή ∀



9>+9+> UBWSB^ CB CJ^SWJGRSJHK BS NHK^HMMISJHK CB^ IRQJFJIJWB^ IR KJPBIR CJ^SWJGRSJHKUIW LWHRUB BK @HKNSJHK CB FI URJ^^IKNB CBMIKCÊB CIK^ FB LWHRUB BS UHRW FB^JKSBWLWHRUB^ BS JKSBW_HKB^

‧ α

‧

‧

‧

9>+9+>+9 Nifnrf cb fi sbmuêwisrwb mhzbkkb cr wê~bir

9>+9+>+9+9 Urj~~iknb khmjkifb cb~ êmbssbrw~ jk~siffê~

k

25

∀ΣΩ25+Ω ⎘

⎥ ⎛

⎖⎝ ⎔

=

∀

∀Σ⎘

⎥

⎛⎖⎝

⎔

∀Σ∗

⎘ ⎥

⎛⎖⎝

⎔

ή

! *! *Ωή

ή=



∀

ι T ]

ιΩ

ΩΩ≢

$=

T ]

T ]

T ]

∀

k

92

@khm∀Σ +92Ω^rwu /wisbmX`w /Ωk` ⎘

⎥ ⎛

⎖⎝ ⎔

=

9

92

@khm∀Σ ^rwu /wisbmX`w /k` U92Ω

∗= ⎘

⎥ ⎛

⎖⎝ ⎔

ή

! *! *Ω92ή

k/U92ήk =

9>+9+>+9+7 Lb~sjhk cr wê~bir cb cj~swjgrsjhk bk mhcb nairc

‧

‧

‧



T ]

α T ]

αα α

T ]ΟΩ

Ω ∀Σ ⎘

⎥

⎛⎖⎝

⎔ =

T ]D khmyp9+90>

ΩNbmbs =

! *

! * 9bmbs∀bmbs (Nbqu

bmbs∀bmbs (NbquNbmbsαiαc∀Σθ

∗Σ

Σ=∗=

α α ∀

α α

α

α

α

≢

α αypXkhm9+90>

Ω

9>+9+>+7 Ubwsb~ cb cj~swjgrsjhk uhrw fb~ wê~birq pbw~ fb~ êmbssbrw~ bs uhrw fb~ wê~birq jksbwlwhrub~ bs jksbwhkb~+

7

αw αcwê~bircrαm

$=

α α T ]

α α T ]

α α T ]

α



9>+9+>+> Nifnrf cb fi nhk~hmmisjhk cb~ njwnrfisbrw~ ~rjpiks fbrw mhcb cb lb~sjhk

9>+9+>+3 Nifnrf cb~ ubwsb~ cb cj~swjgrsjhk wênruêwigfb~

α α

9>+7 CJ^SWJGRSJHK CB @FRJCB @WJLHWJLÁKB



9>+> SWIK^@BWS CB NAIFBRW BKSWB FHNIRQ

9>+>+9 UHMUB^ Å NAIFBRW ^RW GHRNFB C‚BIR

9>+>+7 FB^ ^Z^SÁMB^ Å CÊGJS CB WÊ@WJLÊWIKS PIWJIGFB BS FB^ SABWMH@WJLHUHMUB^



93+ SWIJSBMBKS BS CJ^SWJGRSJHK C,IJW

‧

‧

93+9 UBWSB^ SABWMJYRB^ UHRW FB^ WÊ^BIRQ IÊWIRFJYRB^



93+7 LWHRUB^ C,BQSWINSJHK

93+> NBKSWIFB^ Å CÊGJS ^HR@@FÊ BS BQSWIJS NHK^SIKS BS NBKSWIFB^ CHRGFB@FRQ AZLJÊKJYRB

93+>+9 UWJKNJUB CB UWJ^B BK NHMUSB

‧‧‧‧‧‧

‧

‧



‧

‧

‧

‧

93+>+7 NIFNRF CB F,JMUINS CB^ NHMUH^IKS^

93+>+7+9 Uiwsjb bqswinsjhk



^ênrwjsê iksjlbf

Bnaiklbrw cb naifbrw

Ghësb cb mêfiklb



Pbksjfisbrw

Uwênair``ilb

Uwêwb`whjcj~~bmbks



Armjcj`jnisjhk

Fb~ rkjsê~ cb shjsrwb



93+3 NBKSWIFB^ Å CÊGJS C‚IJW PIWJIGFB MHKH NHKCRJS WB@WHJCJ^^BMBKS ^BRFNAIR@@ILB SBWMJKIF

93+3+9 UWJKNJUB CB UWJ^B BK NHMUSB

‧

‧

93+3+7 NIFNRF CB F‚JMUINS CB^ NHMUH^IKS^

93+3+7+9 Uiwsjb 9

‧ Nifnrf cb~ cêgjs~ mi~~jyrb~ ~hr``fê~ ? mjkjmif bs bk mhcb nair``ilb



‧ Nifnrf cb~ cêgjs~ mi~~jyrb~ wbuwj~ ? mjkjmif bs bk mhcb nair`ìlb

‧ Nifnrf cr cêgjs mi~~jyrb mjkjmif c‚ijw kbr`

‧ Nifnrf cb fi sbmuêwisrwb cb ~hr``filb

Bk hnnruisjhk

cêgjs nair`ìlb wb`whjcj~~bmbks

^z~sámb CIP fhnif

Cêgjs mjkjmif ~hr``fêCêgjs ~hr``fê bk nair`ìlb

Cêgjs ~ruufêmbksijwb bk `whjc

hkb kbrswb

Sj



@jlrwb 95 ? Uwjknjub cb `hknsjhkkbmbks cb fi nbkswifb CIP

≢

Bk jkhnnruisjhk

≢

Sbj

Sirq c‚ijw kbr`

~hr``filb

Uwênair``ilb

Hrpbwsrwb IK Shrs IK

IK mjkjIK mjkj

_hkb kbrswb Wb`whjcj~~bmbks

Sbqssik Sbqswb` Sbkn



93+3+7+7 Uiwsjb 7

‧ Nifnrf cb~ cêgjs~ wêbf~ ~hr``fê bs wbuwj~ ? iuwá~ fb nwhj~bmbks

‧ Nifnrf cb~ cêgjs~ c‚ijw kbr` bk hnnruisjhk bs bk jkhnnruisjhk

≣

≣

‧ Uiwsjb bqswinsjhk



Uwêwb`whjcj~~bmbks

Armjcj`jnisjhk



92+7 UWHCRNSJHK JKCJPJCRBFFB AHW^ PHFRMB NAIR@@Ê

92+> UWHCRNSJHK NHFFBNSJPB WÊ^BIR GHRNFÊ

Urj~~iknb êfbnswjyrb uiw cê`irs cb~ njwnrfisbrw~ uhrw rk wê~bir ghrnfê

⎘⎘ ⎥

⎛⎖⎖⎝

⎔

∀=

miq

+90>9 α

|c

|c

Yy !m>(a* !By 9::*

∀α

+25k+!>k

I+7+7F kjp

25

kjp

hkbcb` X g

⎢⎢⎠

⎣⎧⎧⎮

⎩ ∗$⎘⎘ ⎥

⎛⎖⎖⎝

⎔ = !m* !By 755*

95F+75 u cb` X g g $=∀ !dUi* !By 759*

0>(* u+y!U g|c g X azc ∀= !\* !By 757*

>92(UB`` >735 g X azc|c X njw = !-* !By 75>*



*B`` (U475miq!U |c X njw g X azc|c X njw =

92+3 UWHCRNSJHK NHFFBNSJPB WÊ^BIR SWINÊ



90+ UBWSB^ CB ̂ SHNDILB AHW^ LÊKBWISBRW^ ^SHNDBRW^

‧

‧‧

‧

‧

90+9 NIWINSÊWJ^SISJHK CB^ UWHCRJS^

90+9+9 NAIR@@B BIR ÊFBNSWJYRB^

Sigfbir 23 ? Pifbrw~ uiw cê`irs cb~ ubwsb~ Yu&w bk d\a(ohrw



90+9+7 IRSWB^ GIFFHK^ CB UWHCRNSJHK C‚BIR NAIRCB ÎKJSIJWB UIW INNRMRFISJHK!GIFFHK^ CB ^SHNDILB*

Fb~ giffhk~ c‚BN^ cj~~hnjê~ cb fi uwhcrnsjhk kb ~hks ui~ niwinsêwj~ê~+ Fb~ pifbrw~ cb Nw uwj~b~bk nhmusb ~hks fb~ pifbrw~ uiw cêìrs+

Fb~ pifbrw~ uiw cêìrs ~hks fb~ ~rjpiksb~ ?

Giffhk c‚bir naircb 3&7 + P~ -5&32

Sigfbir 22 ? Pifbrw~ uiw cêìrs cb~ nhk~siksb~ cb wb`whjcj~~bmbks& Nw

90+7 UBWSB^ GWRSB^

Fb~ ubwsb~ c‚rk giffhk ~‚bquwjmbks uiw ?

Yl&| = P~ + Nw + !Sbn~- Simg* ( 73+ !\a* !By 75:*

ipbn ?

P~ = phfrmb cb ~shndilb !f*

Nw = nhk~siksb cb wb`whjcj~~bmbks !\a(f+D+ohrw*

Sbn~ = sbmuêwisrwb cb ~shndilb c‚BN^& uwj~b å 02µN

Simg = sbmuêwisrwb cr fhnif hú b~s ~jsrê fb ~shndilb& uwj~b êlifb å 75 !µN*

90+> UBWSB^ WÊNRUÊWIGFB^

Fb~ ubwsb~ wênruêwigfb~ cb~ giffhk~ cêubkcbks cb f‚bmufinbmbks cr ~shndilb ?

Yl&|Xwbn= Yl&| + Wwbnlbk !d\a* !By 795*

Wwbnlbk b~s fb wbkcbmbks cb wênruêwisjhk cr ~z~sámb cb lêkêwisjhk+

Hk jkobnsb nb~ ubwsb~ ir ui~ cb sbmu~ ~rjpiks+



9<+ LÊKÊWISJHK CB NAIFBRW& CB @WHJC BS C‚BN^

‧

‧‧

‧

‧‧‧

9<+9 ^SWRNSRWB CR NIFNRF

-

-

-

-

-

-



9<+7 NAIWLB CB FI LÊKÊWISJHK

-

-

-

-

-

-

-

-

-

-

-

9<+> SBMUÊWISRWB CB @HKNSJHKKBMBKS CB FI LÊKÊWISJHK CB NAIFBRW UIWLBKBWISBRW Å NHMGR^SJHK

‧

‧

‧



9<+3 NAIWLB CB NAIYRB LÊKÊWISBRW

Mhcb cb lb~sjhk Uwjknjub Bqbmufb

Sigfbir 20 ? Mhcb cb lb~sjhk cb~ uwjhwjsê~ bkswb lêkêwisbrw~

‧ ~j fi lb~sjhk ~b `ijs ~ik~ uwjhwjsê ?

-

‧ ~j fi lb~sjhk ~b `ijs ipbn uwjhwjsê ?

-

-

9<+2 WINNHWCBMBKS CB^ LÊKÊWISBRW^

Winnhwcbmbks cb~ lêkêwisbrw~ ir wê~bir

Sigfbir 2< ? Szub cb winnhwcbmbks ir wê~bir cb~ lêkêwisbrw~



Nb urj~~iknb c‚bkswbsjbk bk \

Sigfbir 2: ? urj~~iknb c‚bkswbsjbk cb~ innrmrfisbrw~ li

9<+0+>

-

-

-

-

-

-

-

9<+0+>+9 Niwinsêwj~isjhk cb~ uwhcrjs~



9<+0+>+9+9 Naircjáwb~ ir li hr ir `jhrf

α

α

Sigfbir 05 ? Niwinsêwj~isjhk cb~ naircjáwb~ ir li bs ir `jhrf



9<+0+>+9+7 Lêkêwisbrw~ c‚ijw nairc

α

Sigfbir 09 ? Niwinsêwj~isjhk cb~ lêkêwisbrw~ c,ijw nairc

9<+0+>+9+> Srgb~ bs uikkbirq wicjiks~

Rkjsê hruh~~jgjfjsê~

Khwmb cbwê`êwbknb

Sigfbir 07 ? Niwinsêwj~isjhk cb~ srgb~ bs uikkbirq wicjiks~



9<+0+>+9+3 Wicjisbrw~ li


Khwmb cbwê`êwbknb

Sigfbir 0> ? Niwinsêwj~isjhk cb~ wicjisbrw~ li

9<+0+>+9+2 Nair``b bir li

Sigfbir 03 ? Niwinsêwj~isjhk cb~ nair``b-bir li

9<+0+>+9+0 Naircjáwb~ ghj~


Khwmb cbwê`êwbknb

Sigfbir 02 ? Niwinsêwj~isjhk cb~ naircjáwb~ ghj~



9<+0+>+7 Pifbrw~ uiw cê`irs

Naircjáwb~ ir lihr ir `jhrf

Naircjáwb~ ghj~

Wicjisbrw~ li

Nair``b-bir li

Innrmrfisbrw~ li

Lêkêwisbrw~c‚ijw nairc li

Srgb~ bs uikkbirq wicjiks~ li

Sigfbir 00 ? Wbkcbmbks~ uiw cê`irs



9<+0+>+> Uwjknjub cb nifnrf

‧

‧

‧

-

-

9<+0+>+3 Mêsahcb lêkêwifb

9<+0+>+3+9 Ubwsb~ å 955" cb naiwlb

! *kUk

Uk

559U

U+W

W -955 Y =



Ni~ uiwsjnrfjbw cb~ naircjáwb~ ir li hr ir `jhrf

α

9<+0+>+3+7 Ubwsb~ uhrw rkb naiwlb jksbwmêcjijwb

Sigfbir 0: ? pifbrw~ uiw cê`irs cb~ naiwlb~ jksbwmêcjijwb~ uhrw fb nifnrf cb~ ubwsb~

! *jks

Ujks

UjksUjks U+

W W -955

Y =

Ni~ uiwsjnrfjbw cb~ naircjáwb~ ir li hr ir `jhrf

α α

α



NaiwlbNaiwlb rsjfb

mjkjmifb

nhk~hmmisjhk

955"

9<+0+>+3+3 Ubwsb~ ir uhjks cb `hknsjhkkbmbks

‧

! * U5U5ksjUjks

qUq YY-Y+

U

U Y $=

! * ksjUksjUU955

jksk

jksqUq YY-Y+

UU

UU Y $

∗

∗=

‧

! * ! * ! * ! *U5

jkskjksk

U5U9557

jksU5ksU7

kq

jkskjksk

U5UjkskU5559Ujks7qUq Y

*U!UUU

Y-YUY-YU+U

*U!UUU

Y-YUY-YU+UY $

∗∗

$∗

∗= j



Srgb~ bs uikkbirq wicjiks~

Sigfbir <> ? Nhb``jnjbks cb miohwisjhk cb~ ubwsb~ uhrw fb~ lêkêwisbrw~ wicjiks~+

9<+0+>+< Nhk~hmmisjhk cb~ irqjfjijwb~ cb lêkêwisjhk

9<+0+>+1 Nifnrf cb~ ubwsb~ wênruêwigfb~

9<+0+>+1+9 Irqjfjijwb~ cb lêkêwisjhk

9<+0+>+1+7 Ubwsb~ cb~ lêkêwisbrw~

Sigfbir <3 ? ubwsb~ uiw fb~ uiwhj~ ~bfhk fb szub cb gwôfbrw



9<+0+>+1+> Shsif cb~ ubwsb~ wênruêwigfb~ cb fi lêkêwisjhk



9<+0+3 LÊKÊWISJHK SABWMHCZKIMJYRB

9<+0+3+9 Bk mhcb nairc

‧

‧



9<+0+3+7 Bk mhcb `whjc

‧



‧

‧

Minajkb~ å nhmuwb~~jhk



Sigfbir <2 ? nhb``jnjbks~ cb nhwwbnsjhk nhkpbksjhkkbf~ uhrw fb~ minajkb~ å nhmuwb~~jhk



Minajkb~ å ig~hwusjhk

Sigfbir <0 ? nhb``jnjbks~ cb nhwwbnsjhk nhkpbksjhkkbf~ uhrw fb~ minajkb~ å ig~hwusjhk

Sigfbir << ? pifbrw~ uiw cê`irs cb~ nhb``jnjbks~ cb nhwwbnsjhk



9<+0+3+3 Cêsbwmjkisjhk cb~ NHU ~ij~hkkjbw~& NHU α b& cb~ minajkb~ ~rw ijw bqsêwjbrw

α

! *! * ⎢

⎠

⎣⎧⎮

⎩$∗

∗= $

∗$$ <

cbl<<> <>+

93+:05 NHU

NHUNHUNHU

jp

! *! * <

cbl<< <+93 $

∗$ $∗∗

= NHUbNHUNHU

NHUjp~~

b α α

! *! * <

>< <+3 $

$ $∗∗

= NHUbNHUNHU

NHU bα α

! * jp

jp

b NHUbNHUNHU

NHU cbl<cbl<> <+

95 ∗∗$ $$

∗= α α



9<+0+3+2 B``bs cb~ irqjfjijwb~

9<+0+3+2+9 Uwê~bksisjhk

9<+0+3+2+9+9 Minajkb~ å nhmuwb~~jhk êfbnswjyrb

‧

‧

‧

‧

‧

‧



9<+0+3+2+7 Mêsahcb cb niwinsêwj~isjhk

9<+0+3+2+7+9 Nhsê minajkb

9<+0+3+2+7+7 Nhsê rsjfj~isjhk

9<+0+3+2+7+> Nhsê bqsêwjbrw

‧

Ϋ

Ϋ

lwhrub shrw

U`

Un

U `whjc

Unhk~hmmêb

Uw

Us



ή

ι

ι Ϋ*

ι Ϋ

ι Ϋ

ι

ι

‧

ι

ι Ϋ

ι Ϋ

9<+0+3+0 Urj~~iknb wê~jcrbffb& Uwê~jcrbffb



9<+0+2 WINNHWCBMBKS Å RK WÊ^BIR CB NAIFBRW

9<+0+2+9 Niwinsêwj~isjhk cb~ uwhcrjs~

9<+0+2+7 Nifnrf cb~ ubwsb~

α α

α

α

α α α

α

α

Szub cb wê~bir Sbmuêwisrwb uwjmijwb αuw~

µNC~~

Sigfbir <1 ? Sbmuêwisrwb uwjmijwb bs nhb``jnjbks C~~ bk `hknsjhk cr szub c‚ênaiklbrw



Nfi~~b c‚j~hfisjhk cb~ nhmuh~iks~ cb fi

~hr~ ~sisjhk ~bfhk fb BK J^H 97171

Sigfbir <: ? Nhb``jnjbks G~~ bk `hknsjhk cr szub c‚j~hfisjhk bs cb fi nisêlhwjb c‚j~hfisjhk

9<+0+2+> Nhk~hmmisjhk cb~ irqjfjijwb~

9<+0+0 WINNHWCBMBKS I RK WÊ^BIR CB @WHJC

9<+< WÊUIWSJSJHK CB^ NHK^HMMISJHK^ UIW R^ILB^



91+ JK^SIFFISJHK^ ^HFIJWB^ SABWMJYRB^

‧

‧

‧

‧

‧

91+9 NAIMU C‚IUUFJNISJHK

‧

‧

‧

‧

‧

‧

‧

‧



91+7 ^SWRNSRWB CB NIFNRF



91+3 NIWINSÊWJ^ISJHK CB^ UWHCRJS^

91+3+9 NIUSBRW^ ̂ HFIJWB^

‧ μ

μ μ

‧ μ

‧

91+3+7 NAIR@@B-BIR ^HFIJWB^

‧ μ

‧

μ



91+3+> GIFFHK^ CB ^SHNDILB

≣

-

-

91+3+3 NI^ UIWSJNRFJBW CR UFIKNABW ^HFIJWB



91+2 BQUWB^^JHK CB FI NHRPBWSRWB ^HFIJWB

91+2+9 @HWMRFB LÊKÊWIFB

Nhb``jnjbks ^shndilb å bir Ufiknabw ~hfijwb

i 957: 5+10> g -5502 -5+9n -5732 -5+70>c 55591 5+551b 55792 5+57:` 5 5+572

Sigfbir 19 ?

∀Σ+

+

μ ∀Σ+

μ μ +

μ∀Σ

μ



91+2+7 NI^ C,RK ^Z^SÁMB NHMGJKÊ !NAIR@@ILB BS BN^*

91+2+> BQUWB^^JHK CB^ UIWIMÁSWB^

91+2+>+9 B``jninjsê cb fi ghrnfb cb niusilb

μμ

μ

91+2+>+7 Cêubwcjsjhk~ sabwmjyrb~ cb fi ghrnfb cb niusilb



91+2+>+0 Nhb``jnjbks nhwwbnsj` c‚jwwjlisjhk cr ~shndilb

Sigfbir 17 ? pifbrw~ cb~ nhb``jnjbks~ n|

91+2+>+< Bk~hfbjffbmbks ~rw fb~ niusbrw~

Sigfbir 1> ? Pifbrw~ mbk~rbffb~ cb f,bk~hfbjffbmbks nhwwjlê ~rw cb~ niusbrw~ pjswê~jknfjkê~ å 32 µbs hwjbksê~ pbw~ fb ~rc !\(m·*



91+0 NIFNRF CB^ UBWSB^ CB SWIK^MJ^^JHK BKSWB FB GIFFHK ^HFIJWB BSF‚IUUHJKS

91+0+9 NAIR@@B-BIR ^HFIJWB JKCJPJCRBF

91+0+7 JK^SIFFISJHK C,BIR NAIRCB ^HFIJWB NHFFBNSJPB Å IUUHJKS NBKSWIFJ^Ê

91+0+> JK^SIFFISJHK C,BIR NAIRCB ^HFIJWB NHFFBNSJPB Å IUUHJKS^ JKCJPJCRBF^



91+< UBWSB^ CB ^SHNDILB CB F‚IUUHJKS

91+<+9 IUUHJKS NBKSWIFJ^Ê !JK^SIFFISJHK NHFFBNSJPB C,BIR NAIRCB ^IKJSIJWB*

91+<+7 IUUHJKS JKCJPJCRBF !JK^SIFFISJHK C,BIR NAIRCB ^IKJSIJWB*

-

- ≢

91+<+> UBWSB^ WÊNRUÊWIGFB^ CB F‚IUUHJKS

91+1 NHK^HMMISJHK CB F‚IUUHJKS

91+: NHK^HMMISJHK CB^ IRQJFJIJWB^ CB F,JK^SIFFISJHK ^HFIJWB

C`hkn = Cbk~ + mjk T 9 4 ! Yna $ Ybn~ * ( !J~n + I + 5&3 + smhj~ * ] Ta]

Cik~ nbssb `hwmrfb& hk nhk~jcáwb yrb& bk ajpbw& fhw~yrb f,bk~hfbjffbmbks wênruêwigfb b~sjk`êwjbrw irq gb~hjk~& fi uhmub uwjmijwb `hknsjhkkb siks yrb fb ~hfbjf gwjffb+ Jkpbw~bmbks&bk êsê& fi uhmub `hknsjhkkb uwhuhwsjhkkbffbmbks ir wiuuhws bkswb fb~ gb~hjk~ bs

f,bk~hfbjffbmbks wênruêwigfb !nb cbwkjbw b~s b~sjmê bk uwbkiks bk nhmusb rk wbkcbmbksmhzbk cr niusbrw ~hfijwb êlif å 35 "*+



Crwêb~ mbk~rbffb~ c,bk~hfbjffbmbks bk abrwb~

91+95 WÊ@ÊWBKNB^ KHWMISJPB^

Jkcjnb cbnfi~~bmbks

Sjswb Urgf

Sigfbir 12 ? wê`êwbknb~ khwmisjpb~



9:+ JK^SIFFISJHK ^HFIJWB UAHSHPHFSIÈYRB^

9:+9 CHMIJKB C‚IUUFJNISJHK

-

-

-

-

9:+7 UWJKNJUB CB NIFNRF

9:+> MÊSAHCB CB NIFNRF



9:+>+9 BKBWLJB JKNJCBKSB AJ

-

-

-

-

-

Sigfbir 10 ? Pifbrw~ cb Aahw&hkb



@S „ _hkb UP3

@S „ _hkb UP2



9:+>+> JKCJNB CB UBW@HWMIKNB WU

-

-

-

-

-

-

Wu

Sigfbir 1: ? Pifbrw~ cb Wu

9:+>+3 BQBMUFB^

Chkkêb~ cr uwhobs Bqbmufb 9 Bqbmufb 7 Bqbmufb >

Nifnrf~ uwêfjmjkijwb~ Bqbmufb 9 Bqbmufb 7 Bqbmufb >

~bfhk Sigfbir 9

~bfhk Sigfbir 7

~bfhk Byrisjhk 7

~bfhk Sigfbir 3

Wê~rfsis~ Wálfb~ SA-N Bqbmufb 9 Bqbmufb 7 Bqbmufb >

~bfhk Byrisjhk9

~bfhk Byrisjhk0

Sigfbir :5 ?



JBN 09030 Bc+ 9+5 Sajk-`jfm sbwwb~swjif uahshphfsijn !UP* mhcrfb~ - Cb~jlk yrifj`jnisjhk ikcszub iuuwhpif

JBN 09792 Bc+ 9+5Nwz~siffjkb ~jfjnhk sbwwb~swjif uahshphfsijn !UP* mhcrfb~ - Cb~jlkyrifj`jnisjhk ikc szub iuuwhpif

Sigfbir :9 ? khwmb~ cb f‚jkcr~swjb uahshphfsièyrb



75+ NHB@@JNJBKS NBU CR GÇSJMBKS

Sigfbir :7 ? Nhb``jnjbks~ cb swik~`hwmisjhk bk êkbwljb uwjmijwb



79+ MÊSAHCB SA-B

79+9 JKSWHCRNSJHK

79+7 MÊSAHCB CB NIFNRF

79+7+9 NIFNRF ^RW FI OHRWKÊB NAIRCB CB WÊ@ÊWBKNB

79+7+9+9 Swik~mjssiknb~ sabwmjyrb~

79+7+9+7 Cêsbwmjkisjhk cb fi sbmuêwisrwb huêwisjpb ahw~ b``bs ~êyrbksjbf

79+7+7 NHWWBNSJHK UHRW F‚B@@BS ̂ ÊYRBKSJBF

79+7+> NIFNRF CB SJN

⎘⎘⎘⎘

⎥

⎛

⎖⎖⎖⎖

⎝

⎔

⎢⎢⎠

⎣

⎧⎧⎮

⎩

$

$=

7

9

7SU

3-

77SU

3-

~byN +3&<0+959

* G9*-!9+N +95+3&<0 !9-9 B +5&<2 CSJ



79+> CHKKÊB^ NFJMISJYRB^

79+>+9 SBMUÊWISRWB BS AZLWHMÊSWJB

79+>+9+9 Pifbrw~ cb wê`êwbknb ir kjpbir cb fi mbw

‧

‧

‧

‧

Sigfbir :> ? Niwinsêwj~sjyrb~ nfjmisjyrb~ cb~ hkb~

79+>+9+7 Nhwwbnsjhk c‚ifsjsrcb



79+>+7+7 Wizhkkbmbks~ ~rw fb~ uiwhj~ khk uwhsêlêb~

79+>+> PJSB^^B CR PBKS

79+3 IUUHWS^ JKSBWKB^

79+2 NIFNRF CB^ CÊGJS^ CB WBKHRPBFFBMBKS C‚IJW

79+2+9 IUUWHNAB LÊKÊWIFB

79+2+7 NIFNRF CR CÊGJS C‚IJW CÔ Å F‚HRPBWSRWB CB^ @BKÏSWB^ BS CB^ HRPWIKS^ ^UÊNJ@JYRB^

α α

α

α α α α

α α

α α

α

Sigfbir :0 ? Pifbrw cb Nsksb



α

α

79+2+> NIFNRF CB FI ^RW@INB FJGWB BK HRPBWSRWB MIKRBFFB

ή

79+2+>+9 Wê~jcbksjbf bs Aêgbwlbmbks ahw~ Bsigfj~~bmbks~ ~ikjsijwb~

Sigfbir :< ? Pifbrw~ cb~ nhb``jnjbks~ Nuw!g&a* bk wê~jcbksjbf

79+2+>+7 Irswb~ gçsjmbks~

Sigfbir :1 ? Pifbrw~ cb~ nhb``jnjbks~ Nuw!g&a* bk khk wê~jcbksjbf



Sigfbir :: ? Pifbrw~ nhkpbksjhkkbffb~ cb Nsksb

79+2+3 NIFNRF CR CÊGJS C‚IJW CÔ Å F‚HRPBWSRWB C,HRPWIKS^ ^UÊNJ@JYRB^ BK JKHNNRUISJHKUHRW FB^ LWHRUB^ Å R^ILB IRSWB YRB C‚AIGJSISJHK BS K‚I^^RWIKS UI^ F‚AÊGBWLBMBKS

79+2+2 ^RWPBKSJFISJHK UHRW FB NHK@HWS C,ÊSÊ

α

α α α α

α α

α α

α



79+0 IUUHWS^ ^HFIJWB^ UIW FB^ GIJB^

79+< NHKPBKSJHK^ CB NIFNRF BS PIFBRW^ UIW CÊ@IRS

79+<+9 WÊ@ÊWBKNB^ WÊLFBMBKSIJWB^ BS KHWMISJPB^ Å RSJFJ^BW

79+<+7 NIWINSÊWJÎSJHK CR ^JSB

79+<+7+9 Niwinsêwj~sjyrb~ nfjmisjyrb~

79+<+7+7 Mi~yrb~ fhjksijk~

79+<+> NIWINSÊWJÎSJHK CR LWHRUB

79+<+>+9 Uwjknjub lêkêwif

79+<+>+7 Pifbrw~ uiw cêìrs uhrw fb~ mi~yrb~

79+<+>+> Hwjbksisjhk~ bs jknfjkij~hk~ uhrw fb~ gijb~



79+<+>+3 Uiwhj~ huiyrb~ bs uhks~ sabwmjyrb~

79+<+>+2 Pbksjfisjhk uiw hrpbwsrwb cb~ `bkïswb~

79+<+>+0 Jkbwsjb



Ikkbqb I Nifnrf cb~ urj~~iknb~ mhzbkkb~ cb pbksjfisbrw~

I+9 ^Z^SÁMB^ Å CÊGJS C‚IJW NHK^SIKS

I+7 ^Z^SÁMB^ Å CÊGJS PIWJIGFB

I+7+9 GÇSJMBKS^ IRSWB^ YRB C‚AIGJSISJHK



I+7+7 GÇSJMBKS^ C‚AIGJSISJHK NHFFBNSJ@^

I+7+7+9 PMN irsh wêlfigfb

I+7+7+7 PMN azlwh wêlfigfb

I+7+> MIJ^HK^ JKCJPJCRBFFB^

I+7+>+9 PMN irsh wêlfigfb

I+7+>+7 PMN azlwh wêlfigfb



Ikkbqb G Nifnrf cb~ ~z~sámb~ c‚êmj~~jhk nhmuh~jsb

G+9 LÊKÊWIFJSÊ^

G+7 ^Z^SÁMB GI^B UFR^ IUUHJKS

Sb bk µN

u i w s i ~ ~ r w ê b u

i w f b ~ z ~ s á m b



G+> NHMUFÊMBKS UIW SBMU^ @WHJC

Sb bk µN

u i w s i ~ ~ r w ê b u i w f b ~ z ~ s á m b

REG2006 méthode réglementaire de calcul thermique des bâtiments RT2005 _FR

Documents

Transcript of REG2006 méthode réglementaire de calcul thermique des bâtiments RT2005 _FR